Solve for $x$ and $y$ using elimination. ${3x+6y = 51}$ ${-3x-5y = -45}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {3x+6y = 51}\thinspace$ to find $x$ ${3x + 6}{(6)}{= 51}$ $3x+36 = 51$ $3x+36{-36} = 51{-36}$ $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ You can also plug ${y = 6}$ into $\thinspace {-3x-5y = -45}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(6)}{= -45}$ ${x = 5}$